Simplify the following expression: $ a = \dfrac{-4}{9} - \dfrac{-6k - 10}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-4}{9} \times \dfrac{7}{7} = \dfrac{-28}{63} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-6k - 10}{7} \times \dfrac{9}{9} = \dfrac{-54k - 90}{63} $ Therefore $ a = \dfrac{-28}{63} - \dfrac{-54k - 90}{63} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-28 - (-54k - 90) }{63} $ Distribute the negative sign: $a = \dfrac{-28 + 54k + 90}{63}$ $a = \dfrac{54k + 62}{63}$